Step 1

Mix chile paste, oil, vinegar, tomato paste, honey, and salt in a small bowl to combine. Cover and chill.Do ahead: Sauce can be made 3 days ahead. Keep chilled.

Step 2

Drain olives in a fine-mesh sieve, discarding any liquid. Thoroughly pat each olive dry (moisture can prevent coating from sticking or cause excess splattering during frying).

Step 3

Whisk flour, cornstarch, baking powder, ¼ tsp. Diamond Crystal or ⅛ tsp. Morton kosher salt, and ¼ cup water in a medium bowl to make the batter. Combine panko and remaining ¼ tsp. Diamond Crystal or ⅛ tsp. Morton kosher salt in another medium bowl. Rub some of the panko between your fingers to create a finer texture.

Step 4

Working with about 5 olives at a time, add to batter and turn to coat. Transfer olives to seasoned panko mixture and turn to coat completely, pressing firmly to adhere. Place on a rimmed baking sheet.

Step 5

Pour oil into a large heavy high-sided skillet to come 1½" up sides. Heat oil over medium-high until an instant-read thermometer registers 400°. Working in batches to avoid crowding the pan and returning oil to 400° after each batch, very carefully lower 10–15 olives into skillet with a slotted spoon and cook until deep golden brown, 1–2 minutes. Transfer olives to paper towels with slotted spoon; sprinkle with sea salt. Let cool 5 minutes, then serve on a plate with sauce.